论文标题
限制平面分段线性系统中的单粒子无穷大周期
Limit cycles from a monodromic infinity in planar piecewise linear systems
论文作者
论文摘要
考虑到具有两个线性区域的平面分段线性系统，该系统被直线分开，并在无穷大时进行了周期性轨道。通过使用变量和参数的一些更改，可以获得具有五个参数的规范形式。通过对可能的周期性轨道的交叉点采取合适的坐标，而不是通常的Bendixson转换以在无穷大近乎无穷大的近乎无穷大的情况下进行工作。表征无穷大的周期轨道稳定性和分叉所需的计算要容易得多。结果表明，无穷大处的HOPF分叉可以具有三个脱粒化的三个，尤其是最多三个极限周期可以从无穷大的周期性轨道分叉。这提供了一种新的机制来解释该系统家族中声称的最大限制周期数量。还分析了无限分类的中心以及从中分叉的极限周期。
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is obtained. Instead of the usual Bendixson transformation to work near infinity, a more direct approach is introduced by taking suitable coordinates for the crossing points of the possible periodic orbits with the separation straight line. The required computations to characterize the stability and bifurcations of the periodic orbit at infinity are much easier. It is shown that the Hopf bifurcation at infinity can have degeneracies of co-dimension three and, in particular, up to three limit cycles can bifurcate from the periodic orbit at infinity. This provides a new mechanism to explain the claimed maximum number of limit cycles in this family of systems. The centers at infinity classification together with the limit cycles bifurcating from them are also analyzed.
